A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = -0.06x^2 + 9.6x + 5.4 where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.
how far horizontally from its starting point will the rocket land? round your answer to the nearest hundred.
the answers are
A 4.30m
B 160.56m
C 161.12m
D 13.94m\
i posted this again because i forgot to put the actual question..oops
it lands when y = 0
0 = -0.06 x^2 + 9.6 x + 5.4 ... use the quadratic formula to find x
... you want the larger positive value
i think b
so would the answer be b? or a?
To find out how far horizontally the rocket will land, we need to determine the value of x when y equals zero. In other words, we need to find the x-intercept of the equation y = -0.06x^2 + 9.6x + 5.4.
To do this, we set y equal to zero and solve for x:
0 = -0.06x^2 + 9.6x + 5.4
This equation is a quadratic equation in the form ax^2 + bx + c = 0, where a = -0.06, b = 9.6, and c = 5.4.
To solve for x, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values a = -0.06, b = 9.6, and c = 5.4, we get:
x = (-(9.6) ± √((9.6)^2 - 4(-0.06)(5.4))) / 2(-0.06)
Simplifying further:
x = (-9.6 ± √(92.16 + 1.296)) / -0.12
Calculating inside the square root:
x = (-9.6 ± √93.456) / -0.12
Taking the square root:
x = (-9.6 ± 9.668) / -0.12
Now we can calculate both possible values of x:
x₁ = (-9.6 + 9.668) / -0.12 ≈ 7.23
x₂ = (-9.6 - 9.668) / -0.12 ≈ -160.53
Since the distance cannot be negative, we can discard the negative value. Thus, the rocket will land approximately 160.53 meters horizontally from its starting point.
Rounding to the nearest hundred, the answer would be 161.00 meters. Therefore, the correct answer is C) 161.12m.